Daily Practice · Higher Plus
May 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 1999 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1999A car covers 880 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.
- 2nd May 1999Use the iteration x(n+1) = cube root of (6x(n) + 2) with x(0) = 2. Work out x(1) to 3 decimal places.
- 3rd May 1999y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 4th May 1999A cuboid measures 15 cm by 5 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th May 1999A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th May 1999A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 7th May 1999Rationalise the denominator of 63/sqrt(7), giving your answer in its simplest form.
- 8th May 1999Work out the nth term of the quadratic sequence 1, 0, 1, 4, ...
- 9th May 1999y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 36.
- 10th May 1999A cuboid measures 12 cm by 9 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th May 1999A bag holds 4 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th May 1999On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 13th May 1999Simplify sqrt(80) + sqrt(125), giving your answer in the form a sqrt(b).
- 14th May 1999The point (-3, -2) lies on y = f(x). Write down its image on y = f(x) + 6.
- 15th May 1999A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.
- 16th May 1999The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 17th May 1999A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 18th May 1999A 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?
- 19th May 1999A rectangle is 30 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th May 1999Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 21st May 1999y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 22nd May 1999In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 23rd May 1999The probability of winning a game is 1/4. A player expects 28 wins. How many games did they play?
- 24th May 1999On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th May 1999Expand and simplify (8 + sqrt(10))(8 - sqrt(10)).
- 26th May 1999f(x) = 3x + 6 and g(x) = 6x + 5. Work out fg(2).
- 27th May 1999y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 28th May 1999In a vector proof you find that vector PQ = a - 3b and vector RS = 2a - 6b. What does this show about PQ and RS?
- 29th May 1999A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 30th May 1999A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 31st May 1999A block has mass 640 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.