Daily Practice · Higher Plus
December 1963 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1963 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1963Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 2nd December 1963y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 3rd December 1963In a vector proof you find that vector PQ = 6a - 2b and vector RS = 30a - 10b. What does this show about PQ and RS?
- 4th December 1963A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 5th December 1963A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 6th December 1963Rationalise the denominator of 16/sqrt(2), giving your answer in its simplest form.
- 7th December 1963f(x) = 4x - 2 and g(x) = 4x + 1. Work out fg(1).
- 8th December 1963y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 36.
- 9th December 1963A cuboid measures 9 cm by 3 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th December 1963A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th December 1963On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th December 1963Simplify sqrt(80) + sqrt(125), giving your answer in the form a sqrt(b).
- 13th December 1963The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 14th December 1963A train slows steadily from 15 m/s to rest in 8 seconds. Work out its deceleration.
- 15th December 1963A cuboid measures 10 cm by 10 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th December 1963A bag holds 6 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th December 1963A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 18th December 1963A rectangle is 14 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th December 1963A quadratic sequence starts 5, 11, 21, 35. Work out the second difference, and the coefficient of n^2.
- 20th December 1963y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 21st December 1963The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 22nd December 1963A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 23rd December 1963On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th December 1963Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
- 25th December 1963Solve x^2 - 2x - 3 > 0.
- 26th December 1963y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 27th December 1963In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 28th December 1963The probability of winning a game is 1/5. A player expects 14 wins. How many games did they play?
- 29th December 1963A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 30th December 1963A block has mass 890 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 31st December 1963Write x^2 + 4x - 8 in the form (x + a)^2 + b.