Daily Practice · Higher Plus
March 1988 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1988 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1988
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1988y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 2nd March 1988A cuboid measures 5 cm by 15 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd March 1988A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th March 1988A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 5th March 1988A car covers 620 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th March 1988Work out the nth term of the quadratic sequence 5, 11, 19, 29, ...
- 7th March 1988y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 25.
- 8th March 1988A cuboid measures 9 cm by 7 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th March 1988A bag holds 4 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th March 1988On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 11th March 1988Rationalise the denominator of 15/sqrt(3), giving your answer in its simplest form.
- 12th March 1988The point (-1, -4) lies on y = f(x). Write down its image on y = f(x) - 4.
- 13th March 1988A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 14th March 1988The 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.
- 15th March 1988A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 16th March 1988A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 17th March 1988Simplify sqrt(32) + sqrt(72), giving your answer in the form a sqrt(b).
- 18th March 1988Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 19th March 1988y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 20th March 1988In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 21st March 1988The probability of winning a game is 1/5. A player expects 10 wins. How many games did they play?
- 22nd March 1988On 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?
- 23rd March 1988A rectangle is 29 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th March 1988f(x) = 4x + 5 and g(x) = 6x + 7. Work out fg(-1).
- 25th March 1988y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 26th March 1988In a vector proof you find that vector PQ = 5a - 2b and vector RS = 20a - 8b. What does this show about PQ and RS?
- 27th March 1988A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 28th March 1988A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 29th March 1988Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 30th March 1988The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 31st March 1988y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 36.