Daily Practice · Higher Plus
February 1990 5-a-day
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The batch download puts all 5 tiers' February 1990 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1990y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 4.
- 2nd February 1990The 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.
- 3rd February 1990A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.
- 4th February 1990On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th February 1990A block has mass 520 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th February 1990Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 7th February 1990A train slows steadily from 24 m/s to rest in 10 seconds. Work out its deceleration.
- 8th February 1990In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 9th February 1990The probability of winning a game is 7/8. A player expects 105 wins. How many games did they play?
- 10th February 1990A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 11th February 1990x = 124 and y = 22, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th February 1990Use the iteration x(n+1) = cube root of (2x(n) + 3) with x(0) = 4. Work out x(1) to 3 decimal places.
- 13th February 1990y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 14th February 1990In a vector proof you find that vector PQ = 6a + 6b and vector RS = 18a + 18b. What does this show about PQ and RS?
- 15th February 1990A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 16th February 1990On 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?
- 17th February 1990A car covers 370 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.
- 18th February 1990Work out the nth term of the quadratic sequence 2, 6, 12, 20, ...
- 19th February 1990y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 20th February 1990A cuboid measures 10 cm by 3 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st February 1990A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd February 1990A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 23rd February 1990Rationalise the denominator of 110/sqrt(11), giving your answer in its simplest form.
- 24th February 1990The point (-6, 3) lies on y = f(x). Write down its image on y = f(x) - 4.
- 25th February 1990y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 4.
- 26th February 1990A cuboid measures 8 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th February 1990A bag holds 7 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th February 1990On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?