2
1 A shape has a rotational symmetry of order two and no lines of symmetry.
Write down the mathematical name of this shape.
.................................................................. [1]
2 Write down all the integers that satisfy this inequality.
.................................................................. [2]
3 Work out (3.7 × 1023) + (3.7 × 1022).
Give your answer in standard form.
................................................ [2]
4 A cuboid has dimensions x cm by x cm by 13 cm.
The volume of the cuboid is 169 cm3.
Find the value of e when x = √𝑒.
e =................................................ [3]
5 Change x cm2 to m2.
Give your answer in the form x(r)-p where r and p are integers to be deduced.
................................................ m2 [2]
3
ADB and AEC are straight lines and BC is parallel to DE.
Show that triangle ABC is similar to triangle ADE.
..............................................................................................................................................................
..............................................................................................................................................................
..............................................................................................................................................................
........................................................................................................................................................ [3]
7 (a) Simplify √300 + √48.
................................................ [2]
(b) Rationalise the denominator and simplify.
................................................ [3]
4
8 The graph shows the cost, in dollars, of buying a length of fabric t metres long.
(a) Samira buys t meters of fabric with a $20 note and receives $1.50 change.
Find the value of t.
Show on the graph how you worked out your answer.
t =................................................ [2]
(b) Anita cuts a length of fabric into two lengths to make a blouse and a skirt.
The lengths of fabric needed to make the blouse and the skirt are in the ratio 5 : 7.
The difference between the lengths of fabric needed to make the blouse and skirt is 5 m.
Find the length of fabric that Anita used to make the blouse.
.............................................. m [3]
5
9 The cost of 20 kilograms of a tropical fruit increases by 10% and then decreases by 15% to give a
new cost of $187.
Find the value of original cost of the 20 kilograms of tropical fruit.
$ .............................................. [3]
10
Find the value of x and the value of y.
x =..............................................
y = ..............................................
[2]
11 f(x) = 3x – 4.
When the domain of f(x) is {0, 5, 7}, find the range of f(x).
............................................................. [2]
6
12 U, V, W, X and Y are points on the circumference of a circle, centre O.
UY is a diameter of the circle and ZX is a tangent to the circle at X.
VUX = 35°, XZY = a° and VWY = b°.
Find an expression for b in terms of a.
Give your answer in its simplest form.
b = ................................................ [4]
7
2
13 The diagram shows the graph of y = – 1.
𝑥
(a) Write down the coordinates of where the graph crosses the x axis.
(............................ , ............................) [1]
(b) Write down the equation of each asymptote.
................................................
................................................
[2]
2
(c) By drawing a suitable straight line on the grid, solve y = – x – 1.
𝑥
x = ............................ or x = ............................ [3]
8
14 (a) Write down the exact value of cos 60°.
................................................ [1]
(b) On the diagram, sketch the graph of y = tanx for values of x between 0° and 360°.
[2]
(c) Solve 2 sinx – 1 = 0 for values of x between 0° and 360°.
x = ............................ or x = ............................ [3]
9
15
16 The area of a parallelogram is 84 cm². Its base is twice as long as its height, x cm.
Find the length of the base in the form w√𝑥 where w and x are integers to be found.
................................................ cm [3]
10
17 The cumulative frequency diagram shows the amount of fuel, f litres, bought by 100 customers at
a service station one day.
(a) Use the diagram to estimate the median.
................................................ litres [1]
(b) Use the diagram to find the fraction of customers who bought more than 30 litres of fuel.
Give your answer in its simplest form.
................................................. [2]
(c) Complete the frequency table for the amount of fuel bought by these 100 customers.
[2]
11
18 The stem-and-leaf diagram shows the mass of each of 13 packets.
Work out the interquartile range.
................................................ g [3]
19 Factorise.
................................................ [1]
20 Information about the time taken by 100 students to solve a puzzle is shown.
Work out an estimate for the mean.
................................................ s [3]
12
21 A vertical line connects point A (4, 10) and point B (4, 2).
Point C (1, 4) and point D (7, 4) lie on a horizontal line that such that quadrilateral ABCD
forms a kite with the diagonals AB and CD intersecting at point O.
The line y = x passes through point O and intersects the kite ABCD at point X that lies on AD.
The distance between point X and point O is √𝑘.
Find the value of k.
k = ................................................ [7]
