smc-4694-10-Expressions

Algebraic Techniques, SM-Bank 030 MC

If $\large x$ is a negative number, which of the following is true?

$x+2$ is always negative.
$x\times -1$ is always negative.
$2-x$ is always negative.
$x-2$ is always negative.

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$D$

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$\text{Considering the options}$

$\text{Option 1: If}\ x\ge -2\ \text{then}\ x+2\ge 0, \therefore \text{not always negative}$

$\text{Option 2:}\ x\ \text{is negative }\therefore x\times -1\ \text{is always positive}$

$\text{Option 3:}\ x\ \text{is negative }\therefore 2-x\ \text{is always positive}$

$\text{Option 4:}\ x\ \text{is negative }\therefore x-2\ \text{is always negative}$

$\Rightarrow D$

Algebraic Techniques, SM-Bank 029

A triangle has a base of length $3$ metres and a perpendicular height of $h$ metres.

Write an expression for the area of the triangle. (2 marks)

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$\dfrac{3h}{2}\ \text{m}^2$

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$\text{Area}$

$=\dfrac{1}{2}\times \text{base}\times\text{perpendicular height}$

$=\dfrac{1}{2}\times 3\times h$

$=\dfrac{1}{2}\times 3h$

$=\dfrac{3h}{2}\ \text{m}^2$

Algebraic Techniques, SM-Bank 028

A rectangle has sides of $b$ metres and $c$ metres in length.

Write an expression for the perimeter of the rectangle. (1 mark)

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Write an expression for the area of the rectangle. (2 marks)

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a. $(2b+2c)\ \text{m}$

b. $bc\ \text{m}^2$

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a. $\text{Perimeter}$

$=b+c+b+c$

$=(2b+2c)\ \text{m}$

b. $\text{Area}$

$=\text{length}\times\text{width}$

$=b\times c$

$=bc\ \text{m}^2$

Algebraic Techniques, SM-Bank 027

A square has sides $x$ centimetres in length.

Write an expression for the perimeter of the square. (1 mark)

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Write an expression for the area of the square. (2 marks)

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a. $4x\ \text{cm}$

b. $x^2\ \text{cm}^2$

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a. $\text{Perimeter}$

$=4\times x$

$=4x\ \text{cm}$

b. $\text{Area}$

$=\text{side}^2$

$=x^2\ \text{cm}^2$

Algebraic Techniques, SM-Bank 026

At the local markets mangoes cost $$x$ and oranges cost $$y$.

Benji bought 6 mangoes and 5 oranges. Write an expression for the total cost of Benji's mangoes and oranges. (2 marks)

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$6x+5y$

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$\text{Total cost}$

$=6\times x +5\times y$

$=6x+5y$

Algebraic Techniques, SM-Bank 025

Juan bought 8 identical Christmas presents online for his relatives.

Write an expression for the total price in dollars, if the cost of each present is $$y$. (1 mark)

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When he goes to the checkout Juan discovers that all the presents were reduced in price by $10 each.

i. Write an expression for the reduced price of one present. (1 mark)

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ii. Write an expression for the total reduced price of all 8 presents. (2 marks)

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a. $8y$

b. i. $y-10$

ii. $8(y-10)$

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a. $\text{Price}=8\times y=8y$

b. i. $\text{Reduced Price per present}=y-10$

ii. $\text{Total Reduced Price}=8\times (y-10)=8(y-10)$

Algebraic Techniques, SM-Bank 024

Rachel works as a waiter and is paid $27 per hour.

Write an expression for her wages in a week where she works $x$ hours. (1 mark)

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$$27x$

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$\text{Wages} = 27\times x =$27x$

Algebraic Techniques, SM-Bank 023

Describe the expression $\dfrac{5}{3q}$ in words. (2 marks)

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$\text{The quotient of 5 and }3q$

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$\text{The quotient of 5 and }3q$

Algebraic Techniques, SM-Bank 022

Describe the expression $(x-y)\times 2$ in words. (2 marks)

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$\text{Twice the difference between }x\ \text{and }y$

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$\text{Twice the difference between }x\ \text{and }y$

Algebraic Techniques, SM-Bank 021

Describe the expression $3y+4$ in words. (2 marks)

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$\text{The sum of 4 and the product of }3\ \text{and }y$

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$\text{The sum of 4 and the product of }3\ \text{and }y$

Algebraic Techniques, SM-Bank 020

Write an expression for subtracting half of $x^2$ from the product of $3$ and $y$. (2 marks)

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$3y-\dfrac{x^2}{2}$

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$\text{Half of }\ x^2=\dfrac{x^2}{2}\ \text{and product }3\ \text{and }y=3y$

$\therefore\ \text{Subtraction}=3y-\dfrac{x^2}{2}$

Algebraic Techniques, SM-Bank 019

Write an expression for one-third of $m$ added to one-fifth of $2n$. (2 marks)

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$\dfrac{m}{3}+\dfrac{2n}{5}$

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$\text{One-third of }\ m=\dfrac{m}{3}\ \text{and one-fifth of }2n=\dfrac{2n}{5}$

$\therefore\ \text{Added together}=\dfrac{m}{3}+\dfrac{2n}{5}$

Algebraic Techniques, SM-Bank 018

Write an expression for the quotient of $2x$ and $z^2$. (1 mark)

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$\dfrac{2x}{z^2}\ \text{ or}\ \ 2x÷z^2$

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$\text{Quotient means divide }$

$\therefore\ \text{quotient of}\ 2x\ \text{and}\ z^2=\dfrac{2x}{z^2}\ \text{ or}\ \ 2x÷z^2$

Algebraic Techniques, SM-Bank 017

Write an expression for 2 added to one-third of $x$. (1 mark)

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$2+\dfrac{x}{3}\ \text{or}\ \ 2+\dfrac{1}{3}x$

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$\text{One-third of }x =\dfrac{x}{3}\ \text{or}\ \ \dfrac{1}{3}x $

$\therefore\ \text{2 added}=2+\dfrac{x}{3}\ \text{or}\ \ 2+\dfrac{1}{3}x$

Algebraic Techniques, SM-Bank 016

Write an expression for a quarter of the sum of $5x$ and $4y$. (1 mark)

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$\dfrac{5x+4y}{4}\ \text{ or }\ \dfrac{1}{4}(5x+4y)$

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$\text{Sum of }5x \text{ and}\ 4y=5x+4y$

$\therefore\ \text{a quarter of the sum}=\dfrac{5x+4y}{4}\ \text{ or }\ \dfrac{1}{4}(5x+4y)$

Algebraic Techniques, SM-Bank 015

Write an expression for double the sum of $a$ and $b$. (1 mark)

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$2\times(a+b)\ \text{or } 2(a+b)$

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$\text{Sum of }a \text{ and}\ b=a+b$

$\therefore\ \text{double the sum}=2\times(a+b) \ \text{or }2(a+b)$

Algebraic Techniques, SM-Bank 014

Write an expression for the product of $3\large xy$ and $-\large y$. (1 mark)

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$-3\large xy^2$

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$\text{Product means multiply}$

$\therefore\ 3xy\times(-y)=-3xy^2$

Algebraic Techniques, SM-Bank 013

Write an expression for the product of $4\large x$ and $\large y$. (1 mark)

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$4\large xy$

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$\text{Product means multiply}$

$\therefore\ \text{product of } 4x$ $\text{and }y=4x\times y=4xy$

Algebraic Techniques, SM-Bank 012

Write an expression for the sum of $-1$ and half of $\large m$. (1 mark)

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$-1+\dfrac{m}{2}\ \ \text{or }\ \dfrac{m}{2}-1$

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$\text{Sum means add}$

$\therefore\ \text{sum of } -1\ \text{and half of } m\ = -1+\dfrac{m}{2}\ \ \text{or }\ \dfrac{m}{2}-1$

Algebraic Techniques, SM-Bank 011

Write an expression for the sum of 5 and 3 lots of $v$. (1 mark)

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$5+3v$

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$\text{Sum means add}$

$\therefore\ \text{the sum of 5 and 3 lots of } \ v\rightarrow 5 +3v$

Algebraic Techniques, SM-Bank 010

State the coefficient of $\large y$ in the expression $2y^3-4y^2+12xy+5y-7$. (1 mark)

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$5$

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$\text{A coefficient is the number in front of a pronumeral}$

$\therefore 5 \text{ is the coefficient of}\ \large y$

Algebraic Techniques, SM-Bank 009

State the coefficient of $\large c$ in the expression $2ab+3b^2-7bc-4c+8$. (1 mark)

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$-4$

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$\text{A coefficient is the number in front of a pronumeral}$

$\therefore -4 \text{ is the coefficient of}\ \large c$

Algebraic Techniques, SM-Bank 008 MC

Which of the following expressions is equivalent to the quotient of $t+8\ $ and $3$?

$\dfrac{t+8}{3}$
$t+11$
$24t$
$3(t+8)$

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$A$

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$\text{Quotient means to divide}$

$\therefore\ \dfrac{t+8}{3} \text{ is equivalent to the quotient of }\ t+8\text{ and }3$

$\Rightarrow A$

Algebraic Techniques, SM-Bank 007 MC

Which of the following expressions is equivalent to the quotient of $2w$ and $7$?

$2w\times 7$
$14w$
$2w-7$
$\dfrac{2w}{7}$

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$D$

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$\text{Quotient means to divide}$

$\therefore\ \dfrac{2w}{7} \text{ is equivalent to the quotient of } 2w\text{ and }7$

$\Rightarrow D$

Algebraic Techniques, SM-Bank 006 MC

Which of the following expressions is equivalent to the product of $x, y$ and $z$?

$x+y+z$
$(xyz)^3$
$xyz$
$\dfrac{xy}{z}$

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$C$

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$\text{Product means to multiply}$

$\therefore\ xyz \text{ is equivalent to the product of } x, y\text{ and }z$

$\Rightarrow C$

Algebraic Techniques, SM-Bank 005 MC

Which of the following expressions is equivalent to the product of $8m$ and $-2$?

$\dfrac{8m}{-2}$
$8m-2$
$-16m$
$-8m+2$

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$C$

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$\text{Product means to multiply}$

$\therefore\ -16m \text{ is equivalent to the product of } 8m\text{ and }-2$

$\Rightarrow C$

Algebraic Techniques, SM-Bank 004 MC

Which of the following expressions is equivalent to the difference between $3y$ and $4$?

$-12 y$
$3 y-4$
$\dfrac{3 y}{4}$
$3y+4$

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$B$

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$\text{Difference means to subtract}$

$\therefore\ 3y-4 \text{ is equivalent to the difference between } 3y\text{ and }4$

$\Rightarrow B$

Algebraic Techniques, SM-Bank 003 MC

Which of the following expressions is equivalent to the difference between $\large x$ and $10$?

$10\large x$
$-\large x$$-10$
$\dfrac{\large x}{10}$
$\large x$$-10$

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$D$

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$\text{Difference means to subtract}$

$\therefore\ \large x$$-10\ \text{is equivalent to the difference between } \large x$$\text{ and }10$

$\Rightarrow D$

Algebraic Techniques, SM-Bank 002 MC

Which of the following expressions is equivalent to the sum of $-5$ and $2x$?

$2x-5$
$-10x$
$\dfrac{2x}{-5}$
$-5-2x$

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$A$

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$\text{Sum means to add}$

$\therefore\ 2x-5\ \text{is equivalent to the sum of } -5\ \text{and}\ 2x$

$\Rightarrow A$

Algebraic Techniques, SM-Bank 001 MC

Which of the following expressions is equivalent to the sum of $3x$ and $4$?

$12x$
$4 + 3x$
$\dfrac{3x}{4}$
$3x-4$

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$B$

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$\text{Sum means to add}$

$\therefore\ 4+3x\ \text{is equivalent to the sum of } 3x\ \text{and}\ 4$

$\Rightarrow B$