Daily Practice · Higher Plus
September 1983 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1983 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1983A cuboid measures 10 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd September 1983A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd September 1983A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 4th September 1983x = 94 and y = 41, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th September 1983Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 6th September 1983y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 7th September 1983The 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.
- 8th September 1983A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 9th September 1983On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th September 1983A car covers 100 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.
- 11th September 1983Use the iteration x(n+1) = cube root of (12x(n) + 6) with x(0) = 2. Work out x(1) to 3 decimal places.
- 12th September 1983y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 13th September 1983In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 14th September 1983The probability of winning a game is 4/5. A player expects 52 wins. How many games did they play?
- 15th September 1983A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 16th September 1983Rationalise the denominator of 15/sqrt(5), giving your answer in its simplest form.
- 17th September 1983Work out the nth term of the quadratic sequence 2, 15, 34, 59, ...
- 18th September 1983y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 9.
- 19th September 1983In a vector proof you find that vector PQ = 2a - 6b and vector RS = 10a - 30b. What does this show about PQ and RS?
- 20th September 1983A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 21st September 1983On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd September 1983Simplify sqrt(20) + sqrt(45), giving your answer in the form a sqrt(b).
- 23rd September 1983The point (0, 2) lies on y = f(x). Write down its image on y = f(x) - 3.
- 24th September 1983A train slows steadily from 31 m/s to rest in 5 seconds. Work out its deceleration.
- 25th September 1983A cuboid measures 10 cm by 6 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th September 1983A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th September 1983A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
- 28th September 1983A rectangle is 17 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th September 1983Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 30th September 1983y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.