Daily Practice · Higher Plus
October 1983 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1983 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1983A cuboid measures 11 cm by 9 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd October 1983A bag holds 7 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd October 1983On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th October 1983Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 5th October 1983f(x) = 2x - 4 and g(x) = 3x + 2. Work out fg(0).
- 6th October 1983y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 7th October 1983The 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.
- 8th October 1983A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 9th October 1983A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 10th October 1983A block has mass 270 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th October 1983The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 12th October 1983y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 9.
- 13th October 1983In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 14th October 1983The probability of winning a game is 2/5. A player expects 4 wins. How many games did they play?
- 15th October 1983On 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?
- 16th October 1983x = 105 and y = 23, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th October 1983A quadratic sequence starts 4, 12, 28, 52. Work out the second difference, and the coefficient of n^2.
- 18th October 1983A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 19th October 1983In a vector proof you find that vector PQ = 2a + b and vector RS = 6a + 3b. What does this show about PQ and RS?
- 20th October 1983A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 21st October 1983A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 22nd October 1983A car covers 210 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 23rd October 1983Solve x^2 + 6x > 0.
- 24th October 1983y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 25th October 1983A cuboid measures 15 cm by 9 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th October 1983A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th October 1983On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th October 1983Rationalise the denominator of 36/sqrt(3), giving your answer in its simplest form.
- 29th October 1983Write x^2 + 16x + 13 in the form (x + a)^2 + b.
- 30th October 1983y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 31st October 1983A cuboid measures 4 cm by 6 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.