Daily Practice · Higher Plus
March 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1993 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1993A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 2nd March 1993A 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?
- 3rd March 1993A rectangle is 4 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th March 1993Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 5th March 1993y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 36.
- 6th March 1993A cuboid measures 15 cm by 8 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th March 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?
- 8th March 1993On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th March 1993Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 10th March 1993Use the iteration x(n+1) = cube root of (5x(n) + 8) with x(0) = 3. Work out x(1) to 3 decimal places.
- 11th March 1993A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 12th March 1993A cuboid measures 13 cm by 9 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th March 1993A bag holds 4 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th March 1993A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 15th March 1993A block has mass 210 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th March 1993Work out the nth term of the quadratic sequence 0, 2, 6, 12, ...
- 17th March 1993y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 18th March 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.
- 19th March 1993A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 20th March 1993On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st March 1993x = 141 and y = 96, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd March 1993The point (0, 4) lies on y = f(x). Write down its image on y = f(-x).
- 23rd March 1993y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 24th March 1993In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 25th March 1993The probability of winning a game is 2/5. A player expects 16 wins. How many games did they play?
- 26th March 1993A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 27th March 1993A car covers 120 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th March 1993Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 29th March 1993y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 36.
- 30th March 1993In a vector proof you find that vector PQ = 4a - 5b and vector RS = 12a - 15b. What does this show about PQ and RS?
- 31st March 1993A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.