Daily Practice · Higher Plus
December 1975 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1975 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1975A bag holds 8 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 2nd December 1975A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 3rd December 1975A rectangle is 29 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th December 1975Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 5th December 1975y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 6th December 1975A cuboid measures 11 cm by 14 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th December 1975A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th December 1975On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th December 1975Expand and simplify (2 + sqrt(10))(2 - sqrt(10)).
- 10th December 1975f(x) = 5x + 2 and g(x) = 4x + 5. Work out fg(4).
- 11th December 1975y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 12th December 1975A cuboid measures 8 cm by 9 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th December 1975A bag holds 6 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th December 1975A 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?
- 15th December 1975A block has mass 650 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.
- 16th December 1975The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 17th December 1975y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 36.
- 18th December 1975The 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.
- 19th December 1975A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 20th December 1975On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st December 1975x = 69 and y = 35, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd December 1975A quadratic sequence starts -2, 3, 14, 31. Work out the second difference, and the coefficient of n^2.
- 23rd December 1975A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
- 24th December 1975In 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.
- 25th December 1975The probability of winning a game is 7/8. A player expects 98 wins. How many games did they play?
- 26th December 1975A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 27th December 1975A car covers 750 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th December 1975Solve x^2 - x - 2 > 0.
- 29th December 1975y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 30th December 1975In a vector proof you find that vector PQ = 4a - 4b and vector RS = 20a - 20b. What does this show about PQ and RS?
- 31st December 1975A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.