Daily Practice · Higher Plus
May 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1993 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1993A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 2nd May 1993x = 61 and y = 38, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd May 1993Work out the coordinates of the turning point of y = x^2 + 2x + 8.
- 4th May 1993y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 5th May 1993A cuboid measures 11 cm by 5 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th May 1993A 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?
- 7th May 1993On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th May 1993A car covers 570 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th May 1993Simplify (x^2 - 49)/(x + 7).
- 10th May 1993y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 11th May 1993A cuboid measures 5 cm by 7 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th May 1993A bag holds 7 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th May 1993A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 14th May 1993Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 15th May 1993In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 16th May 1993y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 25.
- 17th May 1993The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 18th May 1993A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 19th May 1993On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 20th May 1993Simplify sqrt(45) + sqrt(5), giving your answer in the form a sqrt(b).
- 21st May 1993Make x the subject of 5x + 4 = y(x + 4).
- 22nd May 1993A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 23rd May 1993In 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.
- 24th May 1993The probability of winning a game is 3/5. A player expects 15 wins. How many games did they play?
- 25th May 1993A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 26th May 1993A rectangle is 18 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th May 1993Write 4/(x - 2) + 3/(x + 4) as a single fraction.
- 28th May 1993y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
- 29th May 1993In a vector proof you find that vector PQ = 4a + 4b and vector RS = 8a + 8b. What does this show about PQ and RS?
- 30th May 1993A bag holds 8 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 31st May 1993On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?