Daily Practice · Higher Plus
April 2015 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2015 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2015A rectangle is 27 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd April 2015Use the iteration x(n+1) = cube root of (4x(n) + 4) with x(0) = 2. Work out x(1) to 3 decimal places.
- 3rd April 2015y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 64.
- 4th April 2015In a vector proof you find that vector PQ = 4a - 6b and vector RS = 8a - 12b. What does this show about PQ and RS?
- 5th April 2015A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 6th April 2015On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th April 2015Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 8th April 2015Work out the nth term of the quadratic sequence 4, 11, 24, 43, ...
- 9th April 2015A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
- 10th April 2015A cuboid measures 10 cm by 6 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th April 2015A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th April 2015A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 13th April 2015A block has mass 520 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th April 2015The point (1, 3) lies on y = f(x). Write down its image on y = f(x) + 4.
- 15th April 2015y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 16th April 2015A cuboid measures 6 cm by 7 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th April 2015A bag holds 7 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th April 2015On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th April 2015x = 85 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th April 2015Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 21st April 2015y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 22nd April 2015The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 23rd April 2015A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 24th April 2015A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
- 25th April 2015A car covers 680 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th April 2015f(x) = 5x + 2 and g(x) = 6x + 3. Work out fg(5).
- 27th April 2015y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 16.
- 28th April 2015In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 29th April 2015The probability of winning a game is 3/10. A player expects 9 wins. How many games did they play?
- 30th April 2015On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?