Academic Skills Advice
MSU: Test Yourself
Use these questions to test yourself on the whole course. Try to do numbers 1-20 without a calculator.
1.
Calculate: (5 − 3) + 6 × 42 − 20 ÷ 5
2.
Calculate: −12 ÷ 3
3.
Calculate: −10 − 7
4.
Calculate: −3 − (−5)
5.
Calculate: −5 × (−8)
6.
If a water butt holds 210 litres and is full, how much water is in it?
7.
Change
8.
Change 5 3 to an improper fraction.
9.
Work out:
2
3
+5
10.
Work out:
6
7
−
11.
Work out:
6
20
×9
12.
Work out:
2
3
1
13.
5.2 × 100 =
14.
16 ÷ 1000 =
15.
4.7 + 3.9 =
16.
12.7 − 7.82 =
17.
0.03 × 1.2 =
18.
14.4 ÷ 0.3 =
19.
Find 15% of 340.
20.
If an item costs £48, how much will you save in a 20% off sale?
21.
A car priced at £8400 is offered at a reduction of 10%. What is the new price?
22.
The value of a house increased by 60%. If the house was bought for £52,000 how much is it worth
now?
23.
If I read 150 pages of a 200 page book, what percentage have I read?
4
7
22
5
to a mixed number.
2
4
2
3
5
÷6
24.
An item increases in value from £25 to £30. What is the percentage increase?
25.
An item decreases in value from £1200 to £1140. What is the percentage decrease?
26.
Write 5 : 3 as a ratio in its simplest form.
27.
Prize money is shared in the ratio 5:2:1. If the total prize money is £400, how much will be given for
1st, 2nd and 3rd prize?
28.
A smoothie recipe uses strawberries and raspberries in the raio 3:2. If I use 600g of strawberries
what weight of raspberries should I use?
29.
Round 29.1592 to 2 decimal places.
30.
Round 347.52 to 2 significant figures.
31.
Simplify: 3𝑥𝑦 − 4𝑥 + 7𝑦𝑥 + 8𝑦 + 9𝑥
32.
Solve to find 𝑥: 3𝑥 + 5 = 2(5𝑥 − 8)
33.
Calculate: 47
34.
Calculate: √6561
35.
Simplify: 𝑥 3 × 𝑥 8
36.
Simplify: 𝑥 7 ÷ 𝑥 −2
37.
Simplify: (3𝑥 2 )5
38.
Simplify: 7−3
39.
Write 𝑦
40.
Write ( 5√𝑦) as a fractional power.
41.
Write down: 70 =
42.
Write down: 1352 =
43.
Factorise the following as much as possible: 𝑚2 𝑛3 + 𝑚3 𝑛4 − 𝑚2 𝑛2
44.
If 𝑓(𝑥) = 5𝑥 2 − 4𝑥 + 7, find 𝑓(5).
45.
A car hire company uses the following formula to calculate charges: 𝐶 = 25 + 15𝑑. (where C=total
cost and d= number of days.) Calculate the cost to hire a car for 1 week.
46.
Multiply out the brackets: (3𝑥 + 2)(𝑥 − 3)
47.
Solve the simultaneous equations:
2
8
1⁄
3
as a root.
2
2𝑥 − 3𝑦 = 7
3𝑥 + 𝑦 = 5
48.
Solve by using the quadratic formula: 2𝑥 2 − 7𝑥 + 4 = 0
49.
Solve by completing the square: 𝑥 2 − 6𝑥 − 5 = 0
50.
Solve by factorising: 𝑥 2 + 4𝑥 − 21 = 0
51.
Find the 𝑥 and 𝑦 intercepts of the following straight line: 𝑦 = 3𝑥 − 7
52.
Find the equation of the straight line with a gradient of −2 and passing through the point (3,0).
53.
Find the equation of the straight line passing through the points (2,7) and (5,13).
54.
Differentiate: 𝑦 = 2𝑥 3 − 5𝑥 2 + 𝑥 − 7
55.
Given the function 𝑓(𝑥) = 𝑥 3 − 𝑥 2 + 6𝑥 + 5, find the gradient of the function when 𝑥 = 2.
56.
For the following function find where the stationary point is and use the 2nd differential to determine
3
its type: 𝑓(𝑥) = 2 𝑥 2 − 6𝑥 + 4.
57.
Sketch the following quadratic (showing any intercepts and the stationary point): 𝑦 = 𝑥 2 − 7𝑥 + 10.
58.
Sketch the conic: (𝑥 − 2)2 + (𝑦 + 3)2 = 25.
59.
Sketch the conic: 27𝑥 2 + 3𝑦 2 = 27.
60.
Sketch the conic: 25𝑥 2 − 4𝑦 2 = 100.
61.
Use your calculator to find: 𝑙𝑜𝑔6 342
62.
Write as a single log: 3 log(𝑥) + log(𝑦) − 5log⁡(𝑧)
63.
Solve 4𝑥
64.
Solve
65.
If 6𝑥+𝑦 = 36 and 55𝑥+3𝑦 = 1 find 𝑥 and 𝑦.
66.
If 𝑓(𝑥) = 𝑥 2 − 2𝑥 + 3, find 𝑓(𝑥 − 4).
67.
If 𝑔(𝑥) = 𝑥 2 − 7, find 𝑔−1 (𝑥) (the inverse).
68.
Given that 𝑓(𝑥) = 𝑥 2 − 3 and 𝑔(𝑥) = 7𝑥 + 5. Find 𝑓(𝑔(4)).
69.
Given that 𝑓(𝑥) = 𝑥 2 − 3 and 𝑔(𝑥) = 7𝑥 + 5. Find 𝑔(𝑓(𝑥)).
70.
Given the function ℎ(𝑥) = √
2 −5
85𝑥−6
82𝑥+3
= 22 to find 𝑥.
= 12 to find 𝑥.
4
𝑥−2
find the domain and the range.