Fifteen questions across the algebra statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
1.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.
(a)9n + 6
(b)6n
(c)6n + 9
(d)6n + 3
2.Solve 5(x + 3) = 40
(a)x = 8
(b)x = 11
(c)x = 7.4
(d)x = 5
3.The diagram shows the graph of y=x2−x−2, together with the horizontal line y=3. Use the graphs to estimate, to 1 decimal place, the two solutions of x2−x−2=3.
(a)x = −1.8 and x = 2.8
(b)x = −3.0 and x = 4.0
(c)x = 1.8 and x = 2.8
(d)x = −1.0 and x = 2.0
4.A student is proving that (n + 1)² − n² is always an odd number. Which of these correctly completes the first line of algebra?
(a)(n + 1)² − n² = 1
(b)(n + 1)² − n² = 2n + 1
(c)(n + 1)² − n² = 2n
(d)(n + 1)² − n² = n² + 2n + 1
5.Make x the subject of the formula y = (x − 4)/5.
(a)x = 5(y + 4)
(b)x = 5y − 4
(c)x = y/5 + 4
(d)x = 5y + 4
6.A tap fills a tank at a varying rate. A graph shows the rate of flow, in litres per minute, against time, in minutes. What does the area under this graph represent?
(a)The rate at which the flow rate changes, in litres/min².
(b)The total volume of water, in litres, that has flowed in.
(c)The average rate of flow, in litres per minute.
(d)The total time taken to fill the tank, in minutes.
7.A student is asked whether the lines y = (2/5)x − 1 and 5y = −2x + 15 are perpendicular. The student answers: "Yes, because when I rearrange the second equation I get y = −(2/5)x + 3, and 2/5 times −2/5 is negative." Which of these is a correct comment on the student's reasoning?
y = -2x + 15
(a)Wrong — the rearrangement is incorrect.
(b)Right — 2/5 and −2/5 are negatives of each other.
(c)Wrong — the product is −4/25, not −1.
(d)Right — a negative product always means perpendicular.
8.Which of these values of x is a solution of x² + 2x − 15 = 0?
(a)x = 3
(b)x = 5
(c)x = 15
(d)x = −3
9.The graph of y = f(x) has x-intercepts at x = −1 and x = 4. Which statement correctly describes the x-intercepts of y = f(2 − x)?
(a)Translate +2 in x only (no reflection); roots 1, 6
(b)Solved 2 − x = k as x = k − 2; roots −3, 2
(c)No overall change; roots −1, 4
(d)Reflect in the y-axis, +2 in x; roots 3, −2
10.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?
(a)y stays the same however large x becomes
(b)y decreases towards zero but never reaches it
(c)y increases towards a limit but never reaches it
(d)y decreases at a steady rate and reaches zero
11.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
(a)3 and 2n + 5 are the two terms of 6n + 15
(b)6n and 15 are the factors of 6n + 15
(c)3 and 2n + 5 are both factors of 6n + 15
(d)3 is the only factor of 6n + 15
12.A company's cost, in £, for producing x items is shown on a graph. The tangent to the curve at x = 50 passes through (30, 400) and (70, 800). Interpret the gradient of this tangent in the context of the company's costs.
(a)The cost decreases by about £10 per extra item
(b)The cost increases by about £400 per extra item
(c)The cost increases by about £0.10 per extra item
(d)The cost increases by about £10 per extra item
13.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.
(a)£13.20
(b)£15.50
(c)£34.20
(d)£16.70
14.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.
(a)4x = 20
(b)4x − 4 = 20
(c)4x − 4 = 2x + 20
(d)8x − 4 = 20
15.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?