Daily Practice · Higher Plus
September 1990 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1990 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1990A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 2nd September 1990A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 3rd September 1990A block has mass 840 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th September 1990Use the iteration x(n+1) = cube root of (7x(n) + 4) with x(0) = 2. Work out x(1) to 3 decimal places.
- 5th September 1990y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 25.
- 6th September 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.
- 7th September 1990The probability of winning a game is 3/5. A player expects 39 wins. How many games did they play?
- 8th September 1990On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th September 1990x = 45 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th September 1990Work out the nth term of the quadratic sequence 1, 7, 17, 31, ...
- 11th September 1990A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 12th September 1990In a vector proof you find that vector PQ = 4a + 6b and vector RS = 20a + 30b. What does this show about PQ and RS?
- 13th September 1990A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 14th September 1990A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 15th September 1990A car covers 560 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 16th September 1990The point (5, 2) lies on y = f(x). Write down its image on y = f(-x).
- 17th September 1990y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 18th September 1990A cuboid measures 4 cm by 15 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th September 1990A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th September 1990On 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?
- 21st September 1990Rationalise the denominator of 20/sqrt(5), giving your answer in its simplest form.
- 22nd September 1990Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 23rd September 1990y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 24th September 1990A cuboid measures 11 cm by 7 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th September 1990A bag holds 3 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th September 1990A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 27th September 1990Simplify sqrt(27) + sqrt(12), giving your answer in the form a sqrt(b).
- 28th September 1990f(x) = 5x - 3 and g(x) = 5x + 8. Work out fg(4).
- 29th September 1990y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 36.
- 30th September 1990The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.