Daily Practice · Higher Plus
March 1990 5-a-day
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The batch download puts all 5 tiers' March 1990 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1990Simplify sqrt(45) + sqrt(80), giving your answer in the form a sqrt(b).
- 2nd March 1990Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 3rd March 1990A train slows steadily from 39 m/s to rest in 4 seconds. Work out its deceleration.
- 4th March 1990The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 5th March 1990A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 6th March 1990A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 7th March 1990A rectangle is 9 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th March 1990f(x) = 3x - 8 and g(x) = 4x + 6. Work out fg(-1).
- 9th March 1990y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 10th March 1990In 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.
- 11th March 1990The probability of winning a game is 1/4. A player expects 5 wins. How many games did they play?
- 12th March 1990On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th March 1990Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 14th March 1990The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 15th March 1990y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 16th March 1990In a vector proof you find that vector PQ = 6a - 2b and vector RS = 12a - 4b. What does this show about PQ and RS?
- 17th March 1990A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 18th March 1990A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 19th March 1990A block has mass 530 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th March 1990A quadratic sequence starts 5, 7, 11, 17. Work out the second difference, and the coefficient of n^2.
- 21st March 1990y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 9.
- 22nd March 1990A cuboid measures 15 cm by 3 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd March 1990A 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?
- 24th March 1990On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th March 1990x = 141 and y = 47, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th March 1990Solve x^2 + 4x > 0.
- 27th March 1990A train slows steadily from 24 m/s to rest in 10 seconds. Work out its deceleration.
- 28th March 1990A cuboid measures 6 cm by 12 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th March 1990A bag holds 6 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th March 1990A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 31st March 1990A car covers 340 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.