Daily Practice · Higher Plus
March 1989 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1989 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1989Simplify (x^2 + 4x - 12)/(x + 6).
- 2nd March 1989y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 9.
- 3rd March 1989A cuboid measures 13 cm by 5 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th March 1989A bag holds 4 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th March 1989On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th March 1989A block has mass 570 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th March 1989In an algebraic proof, how would you write an even number in terms of an integer n?
- 8th March 1989A train slows steadily from 19 m/s to rest in 10 seconds. Work out its deceleration.
- 9th March 1989The 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.
- 10th March 1989A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 11th March 1989A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 12th March 1989x = 81 and y = 12, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th March 1989Make x the subject of 8x + 4 = y(x + 4).
- 14th March 1989y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 15th March 1989In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 16th March 1989The probability of winning a game is 1/2. A player expects 65 wins. How many games did they play?
- 17th March 1989On 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?
- 18th March 1989A car covers 790 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.
- 19th March 1989Write 7/(x + 3) + 7/(x + 6) as a single fraction.
- 20th March 1989y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 21st March 1989In a vector proof you find that vector PQ = 5a - 2b and vector RS = 20a - 8b. What does this show about PQ and RS?
- 22nd March 1989A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 23rd March 1989A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 24th March 1989Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 25th March 1989Solve 5x^2 + 31x + 30 = 0.
- 26th March 1989y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 25.
- 27th March 1989A cuboid measures 9 cm by 3 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th March 1989A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th March 1989On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th March 1989Simplify sqrt(75) + sqrt(27), giving your answer in the form a sqrt(b).
- 31st March 1989f(x) = 6x - 5. Work out the inverse function f^-1(x).