Number
Insert brackets to make this calculation correct:
32 + 3 × 2 + 5 = 20
32 + (3 × 2) + 5 = 20
Expand and simplify
(2x - 9)(x + 4)
2x2 - x - 36
Find the mode, median and mean from the list:
30, 28, 19, 14, 20, 11, 30, 27, 20, 30
Mode: 30
Median: 23.5
Mean: 22.9
A right-angled triangle has a 39cm hypotenuse and its shortest side is 15cm. Find the length of the unknown side of the triangle.
36cm
90°, 45°, 45°
1823 people attend a concert. Tickets for the concert cost £27.50. Estimate the total revenue from ticket sales and state whether this is an under-estimate or an over-estimate.
£60000, over-estimate
Find the value of x
7x - 3 = 3x + 25
x = 7
Find the mode from the table:
n | f
0 | 3
1 | 15
2 | 9
3 | 11
4 | 2
1
A pizza is 24cm in diameter and is cut into six equal slices. Find the area of each slice to 1dp.
75.4cm2
What is the sum of the angles in a 27-sided polygon?
4500°
Without using a calculator, estimate the value of √150 to one decimal place.
12.2
Find the nth term of the sequence
4, 13, 26, 43, ...
2n2 + 3n - 1
Find the median from the table:
n | f
0 | 3
1 | 15
2 | 9
3 | 11
4 | 2
2
A shipping container is 6m long, 2m wide and 3m deep. It is filled with cube-shaped parcels which are 50cm long. How many parcels can the shipping container hold?
288
Five of the six angles in a hexagon are 104°, 111°, 103°, 126° and 119°. Work out the missing angle.
157°
A tennis ball is served at a speed of 140mph to the nearest 10mph. Write an error interval for the speed s of the tennis ball.
135 ≤ s < 145
Factorise
5x2 + 23x + 12
(5x + 3)(x + 4)
Find the mean from the table:
n | f
0 | 3
1 | 15
2 | 9
3 | 11
4 | 2
A right-angled triangular prism is 3cm tall, 4cm wide and 10cm deep. Work out the surface area of the prism.
132cm2
Two equilateral triangles meet a square and one other regular polygon at a point. How many sides does the other polygon have?
12
Without using a calculator, find the value of 3.7 × 108 - 2.3 × 106. Give your answer in standard form.
3.677 × 108
Find the value of x
x2 - 19x + 84 = 0
x = 7 or x = 12
Jared and Eric both run 5k. Their times for each kilometre are recorded:
Jared:
4:47, 5:01, 5:38, 6:02, 6:27
Eric:
5:32, 5:33, 5:39, 5:35, 5:21
Who is the better runner? Give a reason for your opinion.
Eric is the better runner as his range of times is smaller, showing that he's more consistent. Jared beat Eric's time but each kilometre was slower than the previous kilometre suggesting that he was getting tired quicker than Eric who recorded his best time in the final kilometre.
A football pitch is typically 68m wide.
A footballer takes a corner and it reaches the penalty spot, 11 metres away from the goal-line before the goalkeeper catches it. To the nearest degree, what angle did the footballer take the penalty at?
18°
On whiteboards, draw four diagrams:
One showing two corresponding angles
One showing two alternate angles
One showing two vertically opposite angles
One showing two co-interior angles
All four diagrams must be annotated with the rule associated with each pair of angles.
Corresponding angles are equal
Alternate angles are equal
Vertically opposite angles are equal
Co-interior angles add up to 180°