Daily Practice · Higher Plus
August 1997 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 1997, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 1997 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1997The probability of winning a game is 9/10. A player expects 36 wins. How many games did they play?
- 2nd August 1997On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd August 1997x = 54 and y = 29, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th August 1997Write 6/(x - 6) + 3/(x - 3) as a single fraction.
- 5th August 1997A train slows steadily from 34 m/s to rest in 4 seconds. Work out its deceleration.
- 6th August 1997In a vector proof you find that vector PQ = 3a - b and vector RS = 9a - 3b. What does this show about PQ and RS?
- 7th August 1997A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.
- 8th August 1997A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
- 9th August 1997A car covers 660 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th August 1997Solve 20x^2 - 39x + 18 = 0.
- 11th August 1997y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 12th August 1997A cuboid measures 8 cm by 12 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th August 1997A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th August 1997On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th August 1997Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 16th August 1997f(x) = 2x + 6. Work out the inverse function f^-1(x).
- 17th August 1997y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 18th August 1997A cuboid measures 9 cm by 13 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th August 1997A bag holds 7 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th August 1997A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 21st August 1997Simplify sqrt(8) + sqrt(32), giving your answer in the form a sqrt(b).
- 22nd August 1997Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 23rd August 1997y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 25.
- 24th August 1997The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 25th August 1997A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/3. Work out r.
- 26th August 1997On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 27th August 1997A rectangle is 5 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th August 1997Use the iteration x(n+1) = cube root of (7x(n) + 3) with x(0) = 2. Work out x(1) to 3 decimal places.
- 29th August 1997A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 30th August 1997In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 31st August 1997The probability of winning a game is 2/5. A player expects 14 wins. How many games did they play?