Daily Practice · Higher Plus
December 1961 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1961 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1961The 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.
- 2nd December 1961A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 3rd December 1961A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 4th December 1961A block has mass 760 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.
- 5th December 1961Work out the nth term of the quadratic sequence 5, 9, 19, 35, ...
- 6th December 1961y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 7th December 1961In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 8th December 1961The probability of winning a game is 3/5. A player expects 30 wins. How many games did they play?
- 9th December 1961On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th December 1961x = 34 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th December 1961The point (-5, 1) lies on y = f(x). Write down its image on y = f(x) + 3.
- 12th December 1961y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 13th December 1961In a vector proof you find that vector PQ = 5a + 4b and vector RS = 10a + 8b. What does this show about PQ and RS?
- 14th December 1961A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 15th December 1961A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 16th December 1961A car covers 330 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.
- 17th December 1961Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 18th December 1961y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 25.
- 19th December 1961A cuboid measures 10 cm by 9 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th December 1961A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st December 1961On 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?
- 22nd December 1961Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 23rd December 1961f(x) = 6x + 9 and g(x) = 5x - 8. Work out fg(6).
- 24th December 1961A train slows steadily from 22 m/s to rest in 10 seconds. Work out its deceleration.
- 25th December 1961A cuboid measures 13 cm by 8 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th December 1961A bag holds 6 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th December 1961A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 28th December 1961Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
- 29th December 1961The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 30th December 1961y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 31st December 1961The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.