St#Aloysius#College## # Name: Grade#9#Mathematics ...9+-+CAT+-+Indice… · Apply index laws to...
Transcript of St#Aloysius#College## # Name: Grade#9#Mathematics ...9+-+CAT+-+Indice… · Apply index laws to...
St Aloysius College Name: Grade 9 Mathematics COMMON ASSESSMENT TASK – Indices and Scientific Notation Instructions: You MUST attempt both sections A + B. Neatly show all working out and answers in the space provided. CALCULATOR ALLOWED SECTION A -‐ INDICES
Question 1: Definitions of indices: (3 Marks)
a) State the base of the following: 48 Base = (1)
b) State the power or index of the following: g89 Index = (1)
c) Write the following as a basic numeral: 25 = (1)
Question 2: Use Index Law 1 to simplify the following problems: (8 Marks)
a) 26 × 24 = (1)
b) b7 × b3 = (1)
c) h4 × h5 x h = (1)
d) 2q5 × 3q2 × q10 (2)
e) 5a2b4 × 3a8b5 × 7a6b8 (3)
Question 3: Use Index Law 2 to simplify the following problems: (5 marks)
a) !!
!! = (1)
b) !!
! =
(1)
c) !!!
!!! = (1)
d) !! × !!× !!
!! (2)
Question 4: Use Index Laws 2 + 3 to simplify the following problems: (4 Marks)
a) 30 = (1)
b) 7t0 = (1)
d) !! × !!× !!
!!" = (2)
Question 5: Simplify the following according to index law 4: (5 Marks)
a) (65)3 = (1)
b) (a2b4)3 = (1)
c) (xy4)6 = (1)
d) !!!
!!
! =
(2)
Question 6: Write each of the following with positive indices (e.g. in fractional form) (5 Marks)
a) 2-‐3 = (1)
b) g-‐4 = (1)
c) !!
!! (1)
d) 8r2s-‐5 x 9r-‐3s-‐3 = (2)
Question 7: Write each of the following using a negative index (5 Marks)
a) !! = (1)
b) !!! = (1)
c) !!
!! = (1)
d) 45p2s-‐4 x 3p-‐5s = (2)
Question 8: Simplify (7 Marks)
a) !(!!!)!
!(!!!)! = (2)
b) !!!!!!!!!!
!!!! (2)
c) !!!!
!
!!! ! × !!!!
!
!"! ! (3)
SECTION B – SCIENTIFIC NOTATION
Question 9: Express each of the following numbers using scientific notation (4 Marks)
a) 3000 (1)
b) 6357200 (1)
c) 0.0004 (1)
d) 0.03087 (1)
Question 10: Express each of the following as a decimal number (4 Marks)
a) 5 × 103 (1)
b) 8.047 × 105 (1)
c) 4 × 10-‐4 (1)
d) 3.564 × 10-‐3 (1)
Question 11: The average distance between the moon and Earth is 385000 km (6 Marks)
a) Express this distance in scientific notation (2)
b) How many metres is the moon from the Earth (2)
c) Express the distance of the moon in metres in scientific notation
(2)
Question 12: The mass of a single atom of hydrogen is 1.672621 × 10-‐27 kg. Express this mass as a decimal
(2 Marks)
Australian Curriculum: Mathematics / Year 9 / Number and Algebra / Real Numbers: Apply index laws to numerical expressions with integer indices (ACMNA209)
• simplifying and evaluating numerical expressions, using involving both positive and negative integer indices
Express numbers in scientific notation (ACMNA210)
• representing extremely large and small numbers in scientific notation, and numbers expressed in scientific notation as whole numbers or decimals
Year 9 Achievement Standard (Bolded portion assessed by this test) By the end of Year 9, students solve problems involving simple interest. They interpret ratio and scale factors in similar figures. Students explain similarity of triangles. They recognise the connections between similarity and the trigonometric ratios. Students compare techniques for collecting data in primary and secondary sources. They make sense of the position of the mean and median in skewed, symmetric and bi-‐modal displays to describe and interpret data.
Students apply the index laws to numbers and express numbers in scientific notation. They expand binomial expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment. They sketch linear and non-‐linear relations. Students calculate areas of shapes and the volume and surface area of right prisms and cylinders. They use Pythagoras’ Theorem and trigonometry to find unknown sides of right-‐angled triangles. Students calculate relative frequencies to estimate probabilities, list outcomes for two-‐step experiments and assign probabilities for those outcomes. They construct histograms and back-‐to-‐back stem-‐and-‐leaf plots.