Daily Practice · Higher Plus
May 1997 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 1997, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 1997 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1997A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
- 2nd May 1997In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 3rd May 1997The probability of winning a game is 1/8. A player expects 4 wins. How many games did they play?
- 4th May 1997A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 5th May 1997A block has mass 500 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.
- 6th May 1997f(x) = 3x + 8. Work out the inverse function f^-1(x).
- 7th May 1997y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 8th May 1997In a vector proof you find that vector PQ = 2a + 5b and vector RS = 8a + 20b. What does this show about PQ and RS?
- 9th May 1997A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 10th May 1997On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th May 1997x = 163 and y = 110, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th May 1997Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 13th May 1997y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 14th May 1997A cuboid measures 13 cm by 12 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th May 1997A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th May 1997A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 17th May 1997A car covers 140 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th May 1997Use the iteration x(n+1) = cube root of (12x(n) + 3) with x(0) = 2. Work out x(1) to 3 decimal places.
- 19th May 1997y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 25.
- 20th May 1997A cuboid measures 14 cm by 14 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st May 1997A bag holds 4 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd May 1997On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd May 1997Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 24th May 1997Work out the nth term of the quadratic sequence -6, -2, 6, 18, ...
- 25th May 1997A train slows steadily from 34 m/s to rest in 5 seconds. Work out its deceleration.
- 26th May 1997The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 27th May 1997A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 28th May 1997A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 29th May 1997Simplify sqrt(72) + sqrt(98), giving your answer in the form a sqrt(b).
- 30th May 1997The point (-6, -1) lies on y = f(x). Write down its image on y = f(-x).
- 31st May 1997y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.