Daily Practice · Higher Plus
December 1953 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1953 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1953A cuboid measures 8 cm by 7 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd December 1953A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd December 1953On 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?
- 4th December 1953Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 5th December 1953Solve x^2 + 10x + 21 < 0.
- 6th December 1953y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 7th December 1953A cuboid measures 9 cm by 7 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th December 1953A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th December 1953A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 10th December 1953Simplify sqrt(48) + sqrt(75), giving your answer in the form a sqrt(b).
- 11th December 1953Write x^2 + 10x + 2 in the form (x + a)^2 + b.
- 12th December 1953y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 9.
- 13th December 1953The 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.
- 14th December 1953A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 15th December 1953On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th December 1953A rectangle is 6 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th December 1953Work out the coordinates of the turning point of y = x^2 - 6x + 10.
- 18th December 1953A train slows steadily from 15 m/s to rest in 8 seconds. Work out its deceleration.
- 19th December 1953In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 20th December 1953The probability of winning a game is 3/8. A player expects 15 wins. How many games did they play?
- 21st December 1953A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 22nd December 1953Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 23rd December 1953Simplify (x^2 - 8x + 12)/(x - 6).
- 24th December 1953y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 25th December 1953In a vector proof you find that vector PQ = a + 2b and vector RS = 4a + 8b. What does this show about PQ and RS?
- 26th December 1953A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 27th December 1953On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th December 1953A block has mass 390 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th December 1953In an algebraic proof, how would you write a multiple of 3 in terms of an integer n?
- 30th December 1953y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 31st December 1953A cuboid measures 9 cm by 7 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.