Transformations, SMB-010
Transformations, SMB-009
The point `P(-1, -4)` lies on the Cartesian plane. It is reflected in the `x`-axis to form the point `P^(′)`.
Find the coordinates of `P^(′)`. (1 mark)
Transformations, SMB-008
The point `P(-3, 7)` lies on the Cartesian plane. It is reflected in the `y`-axis to form the point `P^(′)`.
Find the coordinates of `P^(′)`. (1 mark)
Transformations, SMB-007
`P(2,3)` is translated 3 units up and 4 units left.
The new point is then reflected in `x`-axis to form point `P^(′)`.
Find the coordinates of `P^(′)`. (2 marks)
Transformations, SMB-006
`P(-3,-5)` is reflected in the `x`-axis and then translated 3 units to the right to form point `P^(′)`.
Find the coordinates of `P^(′)`. (2 marks)
Transformations, SMB-005
The point `A(-2, 5)` lies on the Cartesian plane. It is translated five units left and then reflected in the `y`-axis.
Find the coordinates of the final image of `A`. (2 marks)
Transformations, SMB-004
The point `P(4, -3)` lies on the Cartesian plane. It is translated four units vertically up and then reflected in the `y`-axis.
Find the coordinates of the final image of `P`. (2 marks)
Linear Applications, SMB-007
Fiona and John are planning to hold a fund-raising event for cancer research. They can hire a function room for $650 and a band for $850. Drinks will cost them $25 per person.
- Write a formula for the cost ($C) of holding the charity event for `x` people. (1 mark)
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- The graph below shows the planned income and costs if they charge $50 per ticket. Estimate the number of guests they need to break even. (1 mark)
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- How much profit will Fiona and John make if 80 people attend their event? (1 mark)
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Linear Applications, SMB-006
The average height, `C`, in centimetres, of a girl between the ages of 6 years and 11 years can be represented by a line with equation
`C = 6A + 79`
where `A` is the age in years. For this line, the gradient is 6.
- What does this indicate about the heights of girls aged 6 to 11? (1 mark)
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- Give ONE reason why this equation is not suitable for predicting heights of girls older than 12. (1 mark)
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Linear Applications, SMB-005 MC
Renee went bike riding on a holiday.
The hiring charges are listed in the table below:
\begin{array} {|l|c|c|}
\hline \text{Hours hired} \ (h) & 1 & 2 & 3 & 4 & 5 \\
\hline \text{Cost} \ (C) & 18 & 24 & 30 & 36 & 42 \\
\hline \end{array}
Which linear equation shows the relationship between `C` and `h`?
- `C = 12 + 6h`
- `C = 6 + 12h`
- `C=18 + 12h`
- `C=12 + 18h`
Linear Applications, SMB-004
Linear Applications, SMB-003 MC
This chart shows the longest run, in kilometres, that Deek ran each week over 5 weeks.
\begin{array} {|l|c|c|c|c|c|}
\hline \textbf{Week} & 1 & 2 & 3 & 4 & 5\\
\hline \textbf{Longest run (km)} & 8 & 11 & 14 & 17 & 20\\
\hline \end{array}
If the pattern continues, in which week is Deek's longest run 29 km?
- `7`
- `8`
- `9`
- `10`
Linear Applications, SMB-002 MC
At an apple orchard, apples are picked and put in a basket.
The table below shows the total number of apples in the basket after each minute.
\begin{array} {|c|c|c|}
\hline \textbf{Minutes} & \textbf{Total number of apples} \\
\hline 1 & 4 \\
\hline 2 & 8 \\
\hline 3 & 12 \\
\hline 4 & 16 \\
\hline \end{array}
How many apples are in the basket after 10 minutes?
- `20`
- `30`
- `35`
- `40`
Linear Applications, SMB-001 MC
Jeremy sold ice creams out of his ice cream truck.
He drew the graph below to show how the number of ice creams he sells in a week is related to their price.
Which statement best describes the graph?
- As the ice cream price goes up, the number sold goes down.
- As the ice cream price goes up, the number sold goes up.
- As the ice cream price goes down, the number sold goes down.
- As the ice cream price goes down, the number sold stays the same.
Cartesian Plane, SMB-021
Cartesian Plane, SMB-020
Prove the points `(1,-1), (-1,1)` and `(-sqrt3,-sqrt3)` are the vertices of a equilateral triangle. (4 marks)
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Cartesian Plane, SMB-019
A straight line passes through points `Q(3,-2)` and `R(-1,4)` .
Find the equation of `QR` and express in general form. (3 marks)
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Cartesian Plane, SMB-018
A straight line passes through points `A(-2,-2)` and `B(1,5)` .
Find the equation of `AB` and express in form `y=mx+b`. (3 marks)
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Cartesian Plane, SMB-017
Cartesian Plane, SMB-016
Calculate the value(s) of `p` given that the points `(p,3)` and `(1,p)` are exactly 10 units apart. (3 marks)
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Cartesian Plane, SMB-015
Calculate the distance between the points `(2,-3)` and `(-5,4)`.
Round your answer to the nearest tenth. (2 marks)
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Cartesian Plane, SMB-014
Calculate the distance between the points `(6,-5)` and `(0,3)`. (2 marks)
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Cartesian Plane, SMB-013
Calculate the distance between the point `(-6,2)` and the origin.
Give your answer in exact form. (2 marks)
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Cartesian Plane, SMB-012
Cartesian Plane, SMB-011
Cartesian Plane, SMB-010
The point `C(-2,3)` is the midpoint of the interval `AB`, where `B` has coordinates `(-1,0).`
What are the coordinates of `A`? (3 marks)
Cartesian Plane, SMB-009
Given `C(-3,-5)` and `D(-5,1)`, find the midpoint of `CD`. (2 marks)
Cartesian Plane, SMB-008
Find `M`, the midpoint of `PQ`, given `P(2, -1)` and `Q(5, 7)`. (2 marks)
Cartesian Plane, SMB-007
On the Cartesian plane below, graph the equation `y-1=-1/2x`.
Clearly label the coordinates of the intercepts with both the `x` and `y`-axes. (2 marks)
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Cartesian Plane, SMB-006
On the Cartesian plane below, graph the equation `y=3x+2`.
Clearly label the coordinates of the intercepts with both the `x` and `y`-axes. (2 marks)
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Cartesian Plane, SMB-005
Cartesian Plane, SMB-004 MC
Cartesian Plane, SMB-003 MC
Cartesian Plane, SMB-002 MC
Transformations, SMB-003 MC
Transformations, SMB-002 MC
Transformations, SMB-001 MC
Linear Relationships, SMB-001 MC
Algebraic Fractions, SMB-060
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)
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