Daily Practice · Higher Plus
November 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2003 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2003The point (0, -1) lies on y = f(x). Write down its image on y = -f(x).
- 2nd November 2003A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
- 3rd November 2003In a vector proof you find that vector PQ = 6a + 3b and vector RS = 24a + 12b. What does this show about PQ and RS?
- 4th November 2003A bag holds 8 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 5th November 2003A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 6th November 2003Simplify sqrt(48) + sqrt(75), giving your answer in the form a sqrt(b).
- 7th November 2003Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 8th November 2003y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 9th November 2003A cuboid measures 3 cm by 14 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th November 2003A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th November 2003On 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?
- 12th November 2003A rectangle is 12 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th November 2003f(x) = 2x + 5 and g(x) = 6x - 4. Work out fg(-3).
- 14th November 2003y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 15th November 2003A cuboid measures 7 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th November 2003A bag holds 6 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th November 2003A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 18th November 2003Expand and simplify (2 + sqrt(10))(2 - sqrt(10)).
- 19th November 2003The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 20th November 2003y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 64.
- 21st November 2003The 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.
- 22nd November 2003A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 23rd November 2003On 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?
- 24th November 2003A block has mass 870 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th November 2003A quadratic sequence starts 9, 15, 27, 45. Work out the second difference, and the coefficient of n^2.
- 26th November 2003A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 27th November 2003In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 28th November 2003The probability of winning a game is 3/4. A player expects 45 wins. How many games did they play?
- 29th November 2003A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 30th November 2003x = 191 and y = 35, each correct to the nearest whole number. Work out the upper bound of x - y.