If `3x-2=(x+1)/5`, find `x`. (2 marks)
Algebraic Fractions, SMB-057
Find the value of `r` given `5-(2r)/3 = 1`. (2 marks)
Algebraic Fractions, SMB-056
If `(n-5)/3 =4-n`, find `n`. (2 marks)
Algebraic Fractions, SMB-055
If `x-(x-3)/2 =4`, find `x`. (2 marks)
Algebraic Fractions, SMB-054
If `(a-2)/5 =2`, find `a`. (2 marks)
Algebraic Fractions, SMB-053
If `(y-3)/2 =5-2y`, find `y`. (2 marks)
Algebraic Fractions, SMB-050
Solve the equation `(2p+2)/3+1 = (p-5)/5`, leaving your answer as a fraction. (3 marks)
Algebraic Fractions, SMB-049
Solve the equation `(x-1)/2+(2x+3)/3 = 2`, leaving your answer as a fraction. (3 marks)
Algebraic Fractions, SMB-048
Solve `(2x+1)/3-(x+1)/8=1` for `x`. (3 marks)
Algebraic Fractions, SMB-047
Solve the equation `(3a)/7 = (2a + 1)/2-3`, leaving your answer as a fraction. (3 marks)
Algebraic Fractions, SMB-046
Solve `(3y-1)/4-(y+1)/3=2` for `y`. (3 marks)
Algebraic Fractions, SMB-052
If `(x-6)/3 =5`, find `x`. (2 marks)
Algebraic Fractions, SMB-051
Find the value of `q` given `q/4-6 = -7`. (2 marks)
Algebraic Fractions, SMB-045
Solve `(2a-5)/3-(a+7)/5=3` for `a`. (3 marks)
Quadratics and Cubics, SMB-044
Solve for `a` given `8a^3+21=0.`
Round your answer to two decimal places. (2 marks)
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Quadratics and Cubics, SMB-043
Solve for `p` given `64p^3+125=0.` (2 marks)
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Quadratics and Cubics, SMB-042
Solve for `x` given `8x^3=27`. (2 marks)
Quadratics and Cubics, SMB-041
By completing the square, solve for `b` given
`b^2-10b-125=0.` (3 marks)
Quadratics and Cubics, SMB-040
By completing the square, solve for `x` given
`x^2-12x=-4.` (3 marks)
Quadratics and Cubics, SMB-039
By completing the square, solve for `y` given
`y^2-14y+37=0.` (3 marks)
Quadratics and Cubics, SMB-038
By completing the square, solve for `x` given
`x^2+4x-1 = 0.` (3 marks)
Quadratics and Cubics, SMB-037
Using the quadratic formula, find `p` given
`p^2+2p-4 = 0.` (3 marks)
Quadratics and Cubics, SMB-036
Using the quadratic formula, find `a` given
`5a^2+7a-1 = 0.` (3 marks)
Quadratics and Cubics, SMB-035
Using the quadratic formula, solve
`3x^2-4x-2 = 0`. (3 marks)
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Quadratics and Cubics, SMB-034
Solve the equation `21-4b^2=5b` for `b.` (2 marks)
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Quadratics and Cubics, SMB-033
Solve the equation `12a^2+8a-15=0` for `a.` (2 marks)
Quadratics and Cubics, SMB-033
Solve the equation `6p^2-p-7=0` for `p`. (2 marks)
Quadratics and Cubics, SMB-032
Solve the equation `6x^2-3x-9=0` for `x`. (2 marks)
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Quadratics and Cubics, SMB-031
Solve the equation `3q^2-10q-8=0` for `q.` (2 marks)
Quadratics and Cubics, SMB-030
Solve the equation `p^2-12p=64` for `p`. (2 marks)
Quadratics and Cubics, SMB-029
Solve the equation `14x=32-x^2` for `x`. (2 marks)
Quadratics and Cubics, SMB-028
Solve the equation `c^2-24=5c` for `c`. (2 marks)
Quadratics and Cubics, SMB-027
Solve the equation `y^2-2y-3=0` for `y`. (2 marks)
Quadratics and Cubics, SMB-025
Solve the equation `t^2-8t+12=0` for `t`. (2 marks)
Non-Linear, SMB-024
The volume of a sphere is given by `V = 4/3 pi r^3` where `r` is the radius of the sphere.
If the volume of a sphere is `220\ text(cm)^3`, find the radius, to 1 decimal place. (3 marks)
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Non-Linear, SMB-023
Make `r` the subject of the equation `V = 4/3 pir^3`. (3 marks)
Inequalities, SMB-022
Solve `4-x/2<=5` if `x` is a negative number.
Graph your solution on a number line. (3 marks)
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Inequalities, SMB-021
Solve `4-x<7`. (2 marks)
Inequalities, SMB-020
Solve `3-x/5<8` if `x` is a negative number. (2 marks)
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Inequalities, SMB-019
Solve `2x+1<7` and graph the solution on a number line. (2 marks)
Inequalities, SMB-018
Solve `1-3x<16` and graph the solution on a number line. (3 marks)
Inequalities, SMB-017
Solve `(4x)/5+1> -1` and graph the solution on a number line. (3 marks)
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Inequalities, SMB-016
Solve `8(x-1)< 10` and graph the solution on a number line. (3 marks)
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Inequalities, SMB-015
Solve `4(x-5)> -14` and graph the solution on a number line. (3 marks)
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Inequalities, SMB-014
Solve `2(x+3)> 12` and graph the solution on a number line. (3 marks)
Inequalities, SMB-013
Solve `2x+1>= -3` and graph the solution on a number line. (3 marks)
Equations, SMB-012 MC
`y = 2x-3`
`y = 4x + 1`
Which value of `x` satisfies both of these equations?
- `x = -2`
- `x = -1`
- `x = 1`
- `x = 2`
Equations, SMB-011
The daily energy requirement, `E` (kilojoules), for a person of mass `m` (kilograms) is calculated using the rule `E = 7m + 7300`.
For Elijah, `E = 7755`.
What is Elijah's mass? (2 marks)
Inequalities, SMB-010
In this inequality `n` is a whole number.
`8/n < 5/8`
What is the smallest possible value for `n` to make this inequality true? (2 marks)
Inequalities, SMB-009
For the expression `x^2 > 5x`, what is the smallest positive whole number `x` can be that makes the expression correct? (2 marks)
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Inequalities, SMB-008
`4/45 = 3/40 + 1/x`
Find the value of `x?` (2 marks)
Inequalities, SMB-007 MC
The weight (`w` kilograms) and age (`a` years) of a turtle are related by the following inequality:
\begin{array} {|l|}
\hline
\rule{0pt}{2.5ex}w < 8a-13\ \ \text{for all values of}\ a\ \text{between 1 and 10}\rule[-1ex]{0pt}{0pt} \\
\hline
\end{array}
Which pair of values satisfy this inequality?
- `w = 4 and a = 2`
- `w = 12 and a = 3`
- `w = 18 and a = 4`
- `w = 40 and a = 6`
Equations, SMB-006
`2/13 < 3/x` where `x` is a positive whole number.
What is the highest possible value for `x`? (2 marks)
Equations, SMB-005
`2(3p-5)-3=17`
Solve for `p`. (2 marks)
Equations, SMB-004
`17y+3(5-3y)-5=26`
What value of `y` makes this equation true? (2 marks)
Equations, SMB-003
`6(3a+4)-12=8a-18`
What value of `a` makes this equation true? (2 marks)
Equations, SMB-002
`2 (4x-2) + 1 +` |
?
|
`= 9x-3` |
What term makes this equation true for all values of `x`? (2 marks)
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Equations, SMB-001
Make `p` the subject of the equation `c = 5/3p + 15`. (2 marks)
Algebra, STD1 A1 2019 HSC 34
Given the formula `C = (A(y + 1))/24`, calculate the value of `y` when `C = 120` and `A = 500`. (3 marks)
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Algebra, STD2 A2 2022 HSC 14 MC
Which of the following correctly expresses `x` as the subject of `y=(ax-b)/(2)` ?
- `x=(2y+b)/(a)`
- `x=(y+b)/(2a)`
- `x=(2y)/(a)+b`
- `x=(y)/(2a)+b`